List of interactive geometry software

Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines, circles or other points. After some construction is done, one can move the points one started with and see how the construction changes.

History

The earliest IGS was the Geometric Supposer, which was developed in the early 1980s. This was soon followed by Cabri and The Geometer's Sketchpad.

Comparison

There are three main types of computer environments for studying school geometry: supposers, dynamic geometry environments (DGEs) and Logo-based programs. Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Geometric Supposer, which does not have draggable objects, but allows students to study pre-defined shapes. Nearly all of the following programs are DGEs.

Licence and platform

The following table provides a first comparison of the different software according to their licence and platform.

2D Software

Software	Licence	Platforms
Baghera	?	Windows/?
Cabri	Commercial	Windows, Mac OS X
Cabri-Euclide	?	Windows/?
C.a.R.	GPL	Windows, GNU/Linux, Mac OS X
CaRMetal	GPL	Windows, GNU Linux, Mac OS X
Cinderella	Commercial	Windows, GNU/Linux, Mac OS X (Java)
Defi	?	?
DrGeo	GPL	GNU/Linux, Mac OS X
Euklid DynaGeo	Shareware	Windows
Euklides	Shareware	Windows
Eukleides	GPL	Windows, GNU/Linux, Mac OS X
Gambol	?	Windows, GNU/Linux, Mac OS X
GCLC	Freeware	Windows, GNU/Linux
GeoGebra	GPL	Windows, GNU/Linux, Mac OS X
Geolog	?	Windows/?
Geometer Sketchpad	Commercial	GNU/Linux, Windows, Mac OS X (Java)
Geometric Supposer	?	?
Geometrix	Freeware	Windows
Geometry Expert (GEX)	?	Windows, GNU/Linux, Mac OS X
Geometry Explorer	?	Windows, GNU/Linux, Mac OS X
Geometry Expressions	Commercial	Windows, GNU/Linux, Mac
Geometry Tutor	?	Windows/?
GeoNext	GPL	Windows, GNU/Linux, Mac OS X
GeoPlan	?	Windows
GeoProof	GPL	Windows, GNU/Linux, Mac OS X
GeoView	GPL	Windows, GNU/Linux, Mac OS X
GEUP	Commercial	Windows
GRACE	?	Windows, GNU/Linux, Mac OS X
iGeom	Freeware	GNU/Linux, Windows, Mac OS X
Isard	?	Windows
Jeometry	?	Windows, GNU/Linux, Mac OS X
JSXGraph	LGPL	Windows, GNU/Linux, Mac OS X
Kig	GPL	GNU/Linux
Kgeo	GPL	GNU/Linux
KmPlot	GPL	GNU/Linux, Mac OS X
KSEG	GPL	Windows, GNU/Linux, Mac OS X
Mathematica	Commercial	Windows, Linux, Mac OS X, Solaris
MathKit	Commercial	GNU/Linux, Windows, Mac OS X (Java)
Mentoniezh	?	?
OpenEuclide	GPL	Windows, GNU/Linux
XCas	GPL	Windows, GNU/Linux, Mac OS X
WinGeom	?	Windows

3D Software

Software	Licence	Platforms
Archimedes Geo3D	Shareware	Windows/Mac OS X/Linux
Cabri 3D	Commercial	Windows/Mac OS X
Geometria	GPL	Windows, GNU/Linux, Mac OS X
GeomSpace	?	Windows
GeomView	LGPL	Unix
Mathematica	Commercial	Windows, Linux, Mac OS X, Solaris
Xcas	GPL	Windows/Mac OS X/Linux
Yenka 3D Shapes	Commercial	Windows

General features

The following table provides a more detailed comparison :

Software	Calculations	Macros	Loci	Animations	Scripting	Assignments	Latex export	Web export	Multilingual	Proofs	Extra
Cabri II Plus	Yes	Yes	Yes	Yes	Yes	Yes (with plug-in)	No	Yes	Yes	Yes (on relations)	Available on TI Calculator
CaR	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No
Cinderella	Yes	Yes	Yes	Yes	Yes	Yes	Yes (PDF)	Yes	Yes	Probabilistic	Several geometries, Physics simulations
GCLC	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No	Yes	Readable proofs, support for 3D
GeoGebra	Yes	Yes	Yes	Yes	Yes (JavaScript)	Yes (JavaScript)	Yes (pstricks)	Yes	35 languages	No	Algebraic manipulations
Geometria	Yes	No	Yes	Yes	No	Yes	No	Yes	Yes	No	Two-role (teacher, student) model
Geometrix	Yes	No	Yes	yes	No	Yes	No	No	No	Yes	Interactive proof, diagram checking, labels with dynamic placeholders
GeoNext	Yes	No	No	Yes	?	?	No	?	Yes	No	Available as a web app
GeoProof	Yes	No	No	No	No	No	Yes	No	No	Yes	Automatic formal proofs
GEUP	Yes	Yes	Yes	Yes	?	No	?	No	Yes	No
iGeom	Yes	Yes	Yes	No	Yes	Yes	No	Yes	Yes	Probabilist	Recurrent scripts
Mathematica	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Full computational system, (geometry and non-geometry), but not a DGS in the common sense
Kig	Yes	Yes	Yes	No	Yes (Python)	No	Yes (pstricks)	No	Yes	No	Labels with dynamic placeholders
Sketchpad	Yes	Yes	Yes	Yes	Yes	No	?	Yes (limited)	Yes	No	Functions & function plots, symbolic differentiation, mathematical notation
Cabri 3D	Yes	No	No	Yes	No	No	No	Yes (limited)	Yes	No
Archimedes Geo3D	Yes	Yes	Yes	Yes	No	No	No	No	No (Eng De Fr)	No	Intersection of Loci
Xcas	Yes	No (programs)	2-d	Yes	Yes	No	Yes	No	Yes	No	Algebraic manipulations
Software	Calculations	Macros	Loci	Animations	Scripting	Assignments	Latex export	Web export	Multilingual	Proofs	Extra

Macros

We detail here the features related to macro constructions. (TODO)

Software	Allows recursity	Allows saving
Cabri II Plus	Yes	Yes
GCLC	Yes	Yes
GeoGebra	Yes	Yes
iGeom	Yes	Yes
Kig	?	Yes
KSEG	Yes	Yes
Mathematica	Yes (programs)	Yes (programs)
Sketchpad (GSP)	Yes (via Iteration)	Yes
XCas	Yes (programs)	Yes (programs)

Loci

We detail here the loci features. (TODO)

Software	Take a point of a locus	Intersection of two loci
Cabri II Plus	Yes	Yes
CaR	Yes	Yes
GeoGebra	Yes	No
iGeom	Yes	No
Kig	Yes	No
Sketchpad (GSP)	Yes	No
Xcas	Yes	Like other parametric curves

Proof

We detail here the proof related features. (TODO)

Software	Interactive Proofs	Automatic Proofs	Probabilist Proofs
Cabri II Plus	Feedback for	No	Yes in Cabri I
Cinderella	No	Using external CAS	Yes
GCLC	Yes	Yes	No
Geometrix	Yes	Yes	No
GeoProof	Yes	Yes	No
iGeom	No	No	Yes
Jeometry	No	Yes	No
Mathematica	No	Using built-in CAS	No
Xcas	No	Using built-in CAS	No

Measurements and calculation

We detail here the measurements and calculation features. (TODO)

Software	Arbitrary Precision	Arithmetic expressions	Trigonometric functions	If	Object existence test
Cabri	Yes	Yes	Yes	Yes	No
C.a.R.	No	Yes	Yes	Yes	Yes
GCLC	No	Yes	Yes	Yes	Yes
GeoGebra	No	Yes	Yes	Yes	Yes (JavaScript)
Geometria	No	Yes	Yes	No	No
GeoProof	Yes	Yes	Yes	Yes	No
Geometrix	No	Yes	Yes	Yes	No
iGeom	No	Yes	Yes	No	No
Mathematica	Yes	Yes	Yes	Yes	Yes
Xcas	Yes	Yes	Yes	Yes	Yes

Graphics Export Formats

Software	PNG	BMP	TIFF	GIFF	SWF	SVG	EMF	Fig	Postscript	Pdf	Latex/Eukleides	Latex/Pstricks
C.a.R.	Yes	No				Yes	No	Yes	Yes	No	No	Yes
Cinderella	Yes	Yes							No	Yes
GCLC	No	Yes				Yes	No	No	Yes	No	No	Yes
GeoGebra	Yes	No				Yes	Yes	No	Yes	Yes	No	Yes
GeoProof	Yes	No				Yes	No	No	No	No	Yes	No
Mathematica	Yes	Yes	Yes	Yes	Yes	Yes			Yes	Yes	Yes	Yes
Kig	Yes	Yes				Yes	No	Yes	Yes	Yes	No	Yes
KmPlot	Yes	Yes				Yes
KSEG	Yes	Yes				$\alpha$	No	No	?	No	No	No
Geometrix	No	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No
iGeom	No	No	No	Yes	No	No	No	No	Yes	No	No	No

Object attributes

Software	Color	Filled/Not filled	Width	Transparency	Shown/Hidden	Layer	Shape of points	Type of line
Cabri	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes
C.a.R.	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
GCLC	Yes	Yes	Yes	No	Yes	No	Yes	Yes
GeoGebra	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Geometria	Yes	Yes	No	Yes	Yes	Yes	No	Yes
Kig	Yes	Yes	Yes	No	Yes	No	Yes	Yes
Mathematica	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes
GeoProof	Yes	No	Yes	No	Yes	Yes	Yes	Yes
Geometrix	Yes	Yes	Yes	No	Yes	No	Yes	Yes
iGeom	Yes	Yes	Yes	No	Yes	No	No	Yes

2D programs

C.a.R.

C.a.R. a free GPL analog of GSP, written in Java.

Plus:

• Multi-platform,
• Multi-lingual,
• Macro-constructions,
• Assignments (good for teachers).

Minus

• Unfriendly measurements,
• Unfriendly loci (trajectories).

CaRMetal

CaRMetal a free GPL software written in Java. It is derived from C.a.R and provides another user interface.

Cabri II Plus

Cabri II Plus an extended analog of GSP and actually the ancestor of all DGSs.

• the more complete locus support, includes intersection of two loci.
• compatible with TI calculators
• based on research on education

Cinderella

Cinderella - very different from GSP, written in Java.

Plus:

• The continuity problem is solved here,
• Switch between elliptic, hyperbolic and Euclidean geometry by one click.
• Two clicks gives projective dual diagram.
• Minor pluses:
  • continuous angle function (can take arbitrary big values).
  • multi-platform.

The new version Cinderella.2 also includes a physics simulation engine and a scripting language. Also, it now supports macros, line segments, calculations, arbitrary functions, plots, etc. Full documentation is available online.

Euklid DynaGeo

Euklid DynaGeo[1] is a shareware analog of GSP for windows.

Minus: There is no function to create a java applet for publishing on web.

Eukleides

Eukleides[2], GPL, is a geometry drawing language.

Plus:

• Macros
• Layers

Minus: There is no function to create a java applet for publishing on web.

Dr Genius

Dr Genius was an attempt to merge Dr. Geo and the Genius calculator

Dr. Geo

Dr. Geo[3] is a GPL interactive software especially valuable for younger students (7-15). Now Dr. Geo II[4] complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.

Plus:

• Macro-constructions

• Embedded scripting

• Programmatically defined interactive drawing

• Customizable interface

• Multilingual

Minus:

• No way to publish objects on the web

Gambol

Gambol[5] is a Euclidean, construction-based, drawing system

GCLC

GCLC[6] is a dynamic geometry tool for visualizing and teaching geometry, and for producing mathematical illustrations. In GCLC figures are described rather than drawn. This approach stresses the fact that geometrical constructions are abstract, formal procedures and not figures. A concrete figure can be generated on the basis of abstract description. There are several output formats, including LaTeX, SVG, PostScript. There is a built-in geometry theorem prover (based on the area method). GCLC is available for Windows and Linux. WinGCLC is a Windows version of GCLC with graphical interface and provides a range of additional functionalities.

GeoGebra

GeoGebra is free software that joins geometry, algebra and calculus for mathematics education in schools.

• License: open source under GNU General Public License (free of charge)
• Languages: 42
• Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines
• Algebra: direct input of cartesian or polar coordinates, linear and quadratic equations; calculations with numbers, points and vectors
• Calculus: direct input of functions; intersections and roots of functions; symbolic derivatives and integrals (built in CAS); sliders as parameters
• Web Export: all constructions exportable as web pages; JavaScript interface for interactive exercises
• Macros: usable both as tools with the mouse and as commands in the input field
• Platforms: Mac OS, Unix/Linux, Windows (anything which supports Java 1.4.2 or later)
• Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects

Geolog

Geolog[7] is a logic programming language for finitary geometric logic.

Geometry Expressions

Geometry Expressions Does symbolic geometry. It uses symbolic inputs and returns symbolic outputs.

Plus:

• Allows algebraic input
• Resolved geometry algebraically and gives symbolic results
• Gives algebraic formulas for measurements
• Constraints supported
• Parametric & implicit equations of loci
• Envelopes of lines & circles
• Supports MathML
• Works with computer algebra systems like Mathematica and Maple

Minus:

• No macros

The Geometer's Sketchpad

The Geometer's Sketchpad (GSP)

• Deterministic
• Languages: English, Spanish, Danish, Russian, Korean, Thai, Traditional and Simplified Chinese, French, Lithuanian (current version); others (older versions).
• Macros: Yes ("custom tools" and "scripts")
• Java-applet: Yes
• Animation: Yes
• Locus: Yes, including point on locus
• Assignments: No
• Measurement/Calculations: Yes
• Platform: Windows, Mac OS, TI-92+, works under wine
• Proofs: No

Geometrix

Geometrix[8] an interactive geometry software, written in Prolog, Free Pascal (Lazarus) and Python. The new french version (3.5) is now free and is being translated into English.

Plus:

• Allows a teacher to propose to a student a specific geometry construction exercise and then the software will check the student's diagram for accuracy.
• Allows the teacher to program specific suggestions in written form, orally and visually via diagrams and short animations of all sort that the teacher can store and have appear at the appropriate times.
• Can automatically generate proof exercises.
• Allows students to do proofs and gives automatic feedback at every step along the way.
• Automatic coding of the figure. Can produce conjectures.
• Dynamic labels : Yes
• Animations : Yes
• Loci : Yes
• Proofs : yes
• Assignements : Yes
• Measurement/Calculations : Yes
• Diagram-checking : Yes
• No-cost software

Minus:

• No macros
• There is no function to create a java applet for publishing on web.

Geonext

Geonext[9] free (GPL) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.

The Geometric Supposer

The Geometric Supposer[10]

GeoProof

GeoProof[11] a free GPL dynamic geometry software, written in Ocaml.

Plus:

• Can import XML files containing a description of a theorem
• Can check if a theorem is true using automated theorem proving methods
• Can help doing proof interactively using the Coq proof assistant
• Can be used to produce high quality figures for latex using Eukleides export
• Dynamic labels
• Computation are done using arbitrary precision
• Layers are available

Minus:

• No locus
• No macros
• There is no function to create a java applet for publishing on web.

GEUP

GEUP bit more calculus-oriented analog of GSP.

• Deterministic
• Languages: English, French, German, Italian, Portuguese, Spanish.
• Macros: Yes
• Java-applet: No
• Animation: Yes
• Locus: Yes / point on locus
• Assignments: No
• Measurement/Calculations: Yes
• Platform: Windows
• Proofs: No

GRACE

GRACE The Graphical Ruler And Compass Editor, an analog of GSP, written in Java.

Plus: includes proof capabilities

iGeom

iGeom[12] - Interactive Geometry on Internet is a freeware software for learning and teaching Geometry (analog of GSP and Cabri), written in Java.

Plus:

• Multi-platform,
• Multi-lingual,
• Macro-constructions, including recurrence (good for fractals constructions),
• Assignments (good for teachers).

Jeometry

Jeometry is a dynamic geometry applet

Isard

Isard[13] is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.

Kig

Kig a free (GPL) analog of GSP for KDE, bit more to calculus-oriented, part of KDE Edutainment Project.

Plus:

• can read simple files from KGeo, KSeg, Dr. Geo and Cabri Geometry (but not very good at this so far).
• builtin support for various types of conics, and for cubics
• basics of differential geometry: tangent line, center of curvature, osculating circle, evolute
• transformations include projective transformations
• poligonal objects (including star polygons like the pentagram) with some operations such as intersection between polygons or line/polygon, convex hull, center of mass

Minus:

• It takes more time to create the same construction than in GSP
• application with "mode": you have to know in which mode you are (normal, constructing, moving, etc)
• there is no function to create a java applet for publishing on web
• no calculations

Kgeo

Kgeo[14] a free (GPL) analog of GSP for KDE, bit more too calculus-oriented, its interface is similar to Kig.

It is no more developed, replaced and improved by Kig.

KmPlot

KmPlot[15] is a mathematical function plotter released under the free (GPL). Includes a powerful parser and precision printing in correct scale. Simultaneously plot multiple functions and combine function terms to build new functions. Supports functions with parameters and functions in polar coordinates. Several grid modes are available.

• powerful mathematical parser
• precise metric printing
• different plot types (functions, parametric, polar)
• highly configurable visual settings (plot line, axes, grid)
• export to bitmap format (BMP and PNG) and scalable vector graphics (SVG)
• save/load complete session in readable xml format
• trace mode: cross hair following plot, coordinates shown in the status bar
• zooming support
• ability to draw the 1st and 2nd derivative and the integral of a plot function
• support user defined constants and parameter values
• various tools for plot functions: find minium/maximum point, get y-value and draw the area between the function and the y-axis

KSEG

KSEG free (GPL) analog of GSP which has a few important unique features. If you plan to do some heavy, complicated constructions in Euclidean geometry this is for you.

• Deterministic
• Languages: Dutch, English, French, Chinese, German, Hungarian, Italian, Japanese, Norwegian Bokmal, Portuguese, Russian, Spanish, Turkish, Welsh.
• Macros: Yes. Editable and with support for recursion
• Java-applet: No
• Animation: No
• Locus: Yes, No direct way to put point on locus.
• Assignments: No
• Measurement/Calculations: Yes (calculator is bit strange)
• Platform: Unix/Linux, Windows, Mac OS (anything which supports Qt)
• Proofs: No
• Extra: Editable

Non-Euclid

Non-Euclid[16] is a very basic Java-IGS only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.

OpenEuclide

OpenEuclide[17] is a GPL 2D geometry software.

Silverlight Dynamic Geometry

Silverlight Dynamic Geometry[18] is written using Silverlight 2 and C# 3.0 (Visual Studio 2008). Only the First Community Technology Preview (First CTP) has been released.

TracenPoche

TracenPoche[19] completely Adobe Flash program. Available in French,English and Spanish.

Tabulae

Tabulae [20] is a dynamic geometry software written in Java. Under development from Federal University of Rio de Janeiro. Available in Brazilian Portuguese.

Wingeom

Wingeom[21] for high-precision geometric constructions in both two and three dimensions

3D programs

Archimedes Geo3D

Archimedes Geo3D

Cabri 3D

Cabri 3D v2

Euler 3D

Euler 3D

Euler 3D is a program that allows you to create and manipulate your own polyhedrons. It has a number of facilities: transformations, animations, creating duals, import/export VRML, etc.

Free registration required.

Geometria

Geometria is free (GPL) cross-platform software based on a two-role (teacher, student) model. The teacher creates a problem, provides it with an answer and saves the problem in a file. The student opens the file and solves the problem. The student's actions are recorded. The teacher plays back the solution and grades it. The figures are limited to convex polyhedra, which can be measured, drawn upon, transformed, cut and joined.

Geomview

Geomview

PyGeo

PyGeo

JavaView

JavaView

JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.

SingSurf

SingSurf

Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.

Doorzien 4

Doorzien 4

A very simple, online applet that allows one to view and bisect a cube in 3D space.

Continuity vs. determinism

All these programs can be divided into two category: deterministic and continuous.

All constructions in the deterministic programs (GSP, Cabri, Kseg and most of others) are completely determined by the given points but the result of some constructions can jump or behave unexpectedly when the a given point is moved.

On the contrary, some constructions in continuous programs (so far only Cinderella), depend on the number of hidden parameters and in such a way that moving a given point produces a continuous motion of the construction, as a result, if the point is moved back to the original position the result of construction might be different.

Here is a test to check whether a particular program is continuous:

Construct the orthocenter of triangle and three mid points (say A', B' C' ) between vertices and orthocenter.

Construct a circumcircle of A'B'C' .

This is the nine-point circle, it intersects each side of the original triangle at two points: the base of altitude and midpoint. Construct an intersection of one side with the circle at mid point now move opposite vertex of the original triangle, if the constructed point does not move when base of altitude moves through it that probably means that your program is continuous.

Although it is possible to make a deterministic program which behaves continuously in this and similar simple examples, in general it can be proved that no program can be continuous and deterministic at the same time.

External links

• Links to the other programs
  • Geometry Software Step-by-step problem solver, download available
  • Geops Free perl script for performing compass and straightedge constructions in the manner of the Ancient Greeks.
  • Geometria An online tool to compute lines, surfaces and volumes of the main plane and solid figures, through direct and indirect formulas.

• Interactive geometry on web:
  • Database of metadata with links to mathematical content
  • Cabri software editor website Available resources for teaching
  • Geometry at cut-the-knot
  • Geometry from the Land of the Incas.
  • Sketchpad Resource Center Including classroom activities, research bibliography, demo version, etc.
  • Free Mathematics Resources Free mathematics resources, ideal for whiteboards
  • The Math Open Reference Project Collection of applets
  • Math tools Catalog of applets
  • Yenka 3D Shapes Free 3D geometry software available to download
  • Interactive geometry examples in Mathematica The Wolfram Demonstrations Project
  • Dynamic Geometry Sketches Includes student explorations and classroom demonstrations.